TEMPERATURE, PRESSURE AND VOLUME 29
in which p, pw are the densities of the dry air and the water vapor, respectively, and cpff the specific heat at constant pressure of water vapor at ordinary temperatures. If, for instance, 3 per cent of the.atmospheric pressure is owing to water vapor, we may put p = 97, pw = 1.866, and find that cp' = 0.2453; substituting this value in equation (5) gives 1° C. per 104.77 meters as the adiabatic gradient so long as the temperature is distinctly above the dew point.
. Clearly, when the temperature of the atmosphere decreases with increase of height at the adiabatic rate, any portion of it transferred without gain or loss of heat from one level to another has, at every stage, the same temperature and density as the adjacent air, and therefore, if abandoned at rest, will neither rise nor fall. If, however, the temperature decreases at a less rate, an isolated mass of air, on being adiabatically lifted or depressed, becomes colder and denser or warmer and rarer, respectively, than the adjacent air, and consequently, if abandoned, will return to its initial level. Finally, if the temperature decreases at a greater rate, an isolated mass of air, on being elevated or depressed, will become warmer and lighter or colder and denser than the adjacent air, and, if permitted, will continue to rise or fall, respectively, until arrested by a change in the temperature gradient, or, if descending, perhaps even by the surface of the earth.
In short, the atmosphere is in neutral, stable, or unstable equilibrium in respect to strictly adiabatic processes according as the temperature decrease with increase of height is the same as, less than, or greater than the adiabatic rate, whatever that may be, or, according as its potential temperature (the temperature any portion would have if brought adiabatically to some given pressure) is constant, increases or decreases with height.
Others, also, of the above equations for dry air have to be appreciably modified to adapt them to the atmosphere as it actually is. Thus, since the various gas constants differ from each other, it is only as an approximation, or under definite conditions, that for the natural air we can write
p = PRT. To be exact we should write, for instance
p = RN(pN + apw + bp0 + • • • • )!F,
in which RN is the gas constant for nitrogen, pN, pw, p0, etc., the current densities of the nitrogen, water vapor, oxygen, etc., respectively, and a, b, etc., the ratios of the density (under like conditions) of nitrogen to those of the several other gases in question. However, as the relative amounts of the chief constituents of the atmosphere, except water vapor, are very nearly constant it is sufficient for all practical purposes to put
7) = R(p H-apJT, (6)